Another option worth considering for regular daily backup is the cloud, using a service like Mozy or Carbonite. Cloud backup has the advantage of distance--since your backup is far away, it won't be lost in the same fire, flood, or burglary that takes your computer. On the other hand, it's painfully slow (the first, initial backup can take weeks) and in the long run costs more.

DVD+R or DVD-R discs work best for long-term archiving of files that aren't likely to change--photos, videos, and so forth. The fact that you can't erase them--a disadvantage for daily backups--is an advantage here. Use good discs (you can buy special archival discs that probably up the chance of their lasting a long time--although there's no way to know for sure). Make multiple copies and keep them in different locations.

If you want to make an image backup of an entire drive or partition, either an external hard drive or DVDs will do. DVDs are cheaper for this very occasional chore, but the hard drive is much more convenient.

Flash is too expensive, on a per-gigabyte basis, for a large-size backup. But it can be handy for copying important files, especially when you're on the road.